Question: Solve for $x$ and $y$ using elimination. ${-3x-5y = -49}$ ${3x-6y = -39}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-11y = -88$ $\dfrac{-11y}{{-11}} = \dfrac{-88}{{-11}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-3x-5y = -49}\thinspace$ to find $x$ ${-3x - 5}{(8)}{= -49}$ $-3x-40 = -49$ $-3x-40{+40} = -49{+40}$ $-3x = -9$ $\dfrac{-3x}{{-3}} = \dfrac{-9}{{-3}}$ ${x = 3}$ You can also plug ${y = 8}$ into $\thinspace {3x-6y = -39}\thinspace$ and get the same answer for $x$ : ${3x - 6}{(8)}{= -39}$ ${x = 3}$